Inferring gene regulatory networks from transcriptomic profiles

1. Dirk Husmeier Inferring gene regulatory networks from transcriptomic profiles Biomathematics & Statistics Scotland

2. Overview • Introduction • Methodology • Circadian regulation in Arabidopsis • Application to synthetic biology • DREAM

3. Network reconstruction from postgenomic data

4. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

5. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

7. Shortcomings Pairwise associations do not take the context of the systeminto consideration direct interaction common regulator indirect interaction co-regulation

8. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

9. 1 2 Direct interaction 1 2 Conditional independence graphs (CIGs) Inverse of the covariance matrix strong partial correlation π12 Partial correlation, i.e. correlation conditional on all other domain variables Corr(X1,X2|X3,…,Xn)

10. Correlation Partial correlation high high high high high low highlow high low

11. 1 2 Direct interaction 1 2 Conditional Independence Graphs (CIGs) Inverse of the covariance matrix strong partial correlation π12 Partial correlation, i.e. correlation conditional on all other domain variables Corr(X1,X2|X3,…,Xn) Problem: #observations < #variables  Covariance matrix is singular

12. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

13. Regulatory network

14. Description with differential equations Concentrations Kinetic parameters q Rates

15. Model Parameters q Probability theory  Likelihood

16. 1) Practical problem: numerical optimization q 2) Conceptual problem: overfitting ML estimate increases on increasing the network complexity

17. Overfitting problem True pathway Poorer fit to the data Equal or better fit to the data Poorer fit to the data

18. Regularization E.g.: Bayesian information criterion (BIC) Regularization term Data misfit term Maximum likelihood parameters Number of parameters Number of data points

19. Likelihood BIC Complexity Complexity

20. Model selection: find the best pathway Select the model with the highest posterior probability: This requires an integration over the whole parameter space:

21. MCMC based schemes q Problem: excessive computational costs

22. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

23. Marriage between graph theory and probability theory Friedman et al. (2000), J. Comp. Biol. 7, 601-620

24. Bayes net ODE model

25. Model Parameters q Bayesian networks: integral analytically tractable!

26. UAI 1994

27. Example: 2 genes 16 different network structures Compute

28. Identify the best network structure Ideal scenario: Large data sets, low noise

29. Uncertainty about the best network structure Limited number of experimental replications, high noise

30. Sample of high-scoring networks

31. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges

32. Sample of high-scoring networks Feature extraction, e.g. marginal posterior probabilities of the edges Uncertainty about edges High-confident edge High-confident non-edge

33. Sampling with MCMC Number of structures Number of nodes

34. UAI 1994

35. Model Parameters q Bayesian networks: integral analytically tractable!

36. Linearity assumption [A]= w1[P1]+ w2[P2] + w3[P3] + w4[P4] + noise P1 w1 P2 A w2 w3 P3 w4 P4

37. Homogeneity assumption Parameters don’t change with time

38. Homogeneity assumption Parameters don’t change with time

39. Limitations of the homogeneity assumption

40. Overview • Introduction • Methodology • Circadian regulation in Arabidopsis • Application to synthetic biology • DREAM

41. Accuracy Mechanistic models Bayesian networks Conditional independence graphs Methods based on correlation and mutual information Computational complexity

42. Example: 4 genes, 10 time points

43. Standard dynamic Bayesian network: homogeneous model

44. Limitations of the homogeneity assumption

45. Our new model: heterogeneous dynamic Bayesian network. Here: 2 components

46. Our new model: heterogeneous dynamic Bayesian network. Here: 3 components

47. Extension of the model q

48. Extension of the model q Allocation vector h k Number of components (here: 3)

49. Analytically integrate out the parameters q Allocation vector h k Number of components (here: 3)

50. Non-homogeneous model  Non-linear model